A cmg fine attitude control system

ABSTRACT

The invention teaches an attitude control system for providing control torques on a vehicle, such as a space satellite, using four single gimbal control moment gyroscopes. The relatively simple constant-gain steering law permits three axis control after failure of any one of the four control moment gyroscopes.

United StatesPatent n 1 [1 1 3,741,500

Liden June 26, 1973 [54] CMG FINE ATTITUDE CONTROL 3,493,194 2/1970Kurzhals 244 1 SA YS M 3,489,004 1/1970 Barnhill et al. 74/534 X3,547,381 12/1970 Inventor: Sam Liden, Phoemx, Arlz- 3,452,948 7/1969Kukel et al. 244/1 SA [73] Assignee: Sperry Rand Corporation, New

York, Primary Examiner-Duane A. Reger 22 Filed: p 21 1971 AssistantExaminer-Stephen' G. Kunin Attorney--S. C. Yeaton [21] Appl. No.:136,088

52 us. Cl..; 244/1 SA, 33/226 2, 74/534, [571 ABSTRACT [51] Int i 2 33?The invention teaches an attitude control system for l 581 Fie'm 7 34providing control torques on a vehicle, such as a space satellite, usingfour single gimbal control moment gyro- 1 Ins/489 scopes. The relativelysimple constant-gain steering law permits three axis control afterfailure of any one of the [56] References Cited I four control momentgyroscopes. UNITED STATES PATENTS 3,329,375 7/l967 Kurzhalset al. 244/]SA 3 Claims, 5 Drawing Figures 53 51 S 3 m wm mauzuvzn COMMAND d 5COMPUTER 9 61 62 64 55 v 5S8 60 5 s EULER 5752mm; c CMG T VEH'CLE w c oi irl a COPTFIG.

63x szusons PATENTED M26 I973 SHEEI1B3 A TTOR/VEY A CMG FINE ATTITUDECONTROL SYSTEM BACKGROUND OF THE INVENTION 1. Field of the Invention Theinvention relates to a configuration of control moment gyroscopesutilizing a relatively simple constant-gain steering law which permitsthree axis control after failure of one gyroscope.

2. Description of the Prior Art Previous control moment gyroscopeconfigurations can operate under simple control computations but requiresix single gimbal control moment gyroscopes. However, they do notprovide or permit a fail operational configuration without considerablemodification of the control computations. Other control moment gyroscopeconfigurations may provide fail operational configurations with four ormore single gimbal control moment gyroscopes, or three or more doublegimbal control moment gyroscopes, but the control computations arehighly complex. In addition, previously known gyro/gimbal configurationsrequire one spare gyroscope for each primary gyroscope which duplicatesthe orientation of each primary gyroscope in order to maintain fulloperational capability after a failure of any of the primary gyroscopes.

SUMMARY OF THE INVENTION In the four single gimbal fine attitude controlsystem (4-FACS), the control moment gyroscopes (CMGs) are arranged intwo pairs, where the two gimbal axes in each pair are parallel orcollinear, and where the gimbal axes of one pair are typicallyperpendicular to the gimbal axes of the other pair. The gimbal axes liein the yz-plane of the CMG system coordinates, with angles of 45, 135,225 and 315 from the y-axis and coun-- terclockwise about the x-axis.This configuration permits the use of a relatively simple constant gainsteering law. The angular relationships between the gimbals and- BRIEFDESCRIPTION OF THE DRAWINGS A preferred embodiment of the presentinvention is illustrated in the accompanying drawings wherein:

FIG. 1 is a schematic illustration of the CMG configuration and itsorientation relative to a set of reference axes;

FIG. 2 is a diagram illustrating relative orientations of the CMGmomentum vectors relative to the refer ence axes;

FIG. 3 is an electrical schematic illustrating an implementation of thesteering law of the present invention;

FIG. 4 is a schematic block diagram of an implementation of a modifiedsteering law; and I FIG. 5 is a block diagram of a complete vehiclecontrol loop embodying the steering-law of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT Space satellites are oftenrequired to maintain a fixed orientation while in orbit to accomplishthe mission. Examples of such requirements may be that of positioningsolar cells most favorably in relation to the sun, positioning areflective antenna in respect to a transmitter and a receiver, ortracking objects by optical or electronic methods. The nature of thesetypes of missions is that not only must corrections be made for gradualor relatively slow reorientation about one or more axes of the spacevehicle or station due to external disturbances, but there must alsoexist a capability for rapid reorientation of the vehicle, for example,to permit a capture of a new tracking target. Thus, the control functionmust be capable of providing not only a high angular momentum, butcontrolling it with a great dcgree of precision.

between the gimbal pairs may be modified if-it is desired to modify therelative angular momentum capacity of the configuration, without undulycomplicating the steering law.

In operation, both the magnitude and direction of the net angularmomentum vector of the control moment gyro system is controlled bycontrolling the relative magnitude and direction of the resultantangular momentum of each pair of gyros, each pair being arranged as ascissored pair.

A primary object of the invention is'to provide an attitude controlsystem for a CMG controlled vehicle using a constant gain steering law.

Another object of the invention is to provide a CMG configurationwherein only minor modifications of the steering law are required whenconverting from a four gyro operation to a three gyro operation.

Another object of'the invention is to provide asteering law easilymodifiable to include additional tolerance control capability.

Another object of the invention is to provide a control moment gyroscopesystem capable of using the total available angular momentumof allgyroscopes in one axis.

Another object of the invention is to provide standby redundancy withonly two additional gyros.

Referring to FIG. 1, which is a simple and convenient illustration ofthe gimbal orientation of the CMGs,

there is shown a fine attitude control system consisting of foursingle-gimbal control moment gyroscopes (CMGs) arranged generally as twoscissored pairs. Each gyro assembly comprises a high momentum rotor (notshown) journalled in a rotor bearing case or gimbal. As shown, thegimbal support axes in each pair are parallel or collinear and thegimbal axes of one pair are typically perpendicular to the gimbal axesof the other pair. The three axes shown, x, y, z correspond to thevehicle control axes, but not necessarily the conventional xyz axes ofthe vehicle. The gimbal axes as shown lie in the yz plane of the CMGcoordinate system with angles of 45, 135, 225 and 315 from the y-axis,progressing counterclockwise about the x-axis. The angle between eachpair of gimbal axes may be altered from the configuration shown if it isdesired to modify the relative angular momentum capacity of theconfiguration in the y and z axes. Additionally, the gimbal axis of eachpair of gyros may be other than parallel to each other andstill providesatisfactory operation under the steering law (to be discussed) of thissystem, however, additional coupling between axes is introduced anddetracts from the optimum mode of operation. It is to be 7 understoodthat the CMGs may betranslated in any direction so long as the fixedangular relation to each other is maintained without departing from thescope of the invention.

The angular momentum vectors of each of the CMGs depicted as emanatingfrom the center of each.

shown. The explanation of the steering law may be simplified if eachpair of gyroscopes having collinear axes are considered as a scissoredpair. The angular momentum vector of gyros 1 and 3 is denoted as H, andthat of gyros 2 and 4 by H,,. The orthogonal semicircular illustrationsindicate the planes within which H, and H may rotate, but it is to beunderstood that under certain modifications of the stbering law, thevectors H,, and H, may rotate more than 180. For the initial gimbal angles, a H, lies in the +x direction, H,, lies in the x direction, andeach has the magnitude of V3 11, where h is the angular momentum of eachgyro (assuming all are equal). By expanding this proposition, themagnitude of H is 2h sin [(01 a )/2] and H,, is 2h sin [(01 a.,)/2] andthe angles of H, from the +x axis is a,,, where a, (at a;,)/2 and theangle of H, from the x axis is a,,, where 01,, a, a )/2.

In operation, the vectors H, and H, cooperate to produce the net angularmomentum, which ultimately is used to reorient the space vehicle. Wheneither H or H, is changed in either magnitude or angular orientation,the net angular momentum is affected. In example, to produce a netangular momentum, H, in the +x direction, starting from the initialcondition of a the magnitude of H,, is increased by increasing a, and04;, by equal amounts and the magnitude of H,, is decreased byincreasing a and by equal amounts. To produce H in the +y direction,01,, and 01,, are increased by equal amounts and the magnitudes of H andH,, are held constant. To produce H in the +z direction, or,, isdecreased and 01,, is increased by an equal amount and the magnitudes ofH,, and H,, are held constant. To produce an H in a direction other thanalong a primary axis, combinations of the above movements are effected.

In a situation where one gyro has failed, the remaining gyro in thatpair is reoriented such that its H v ctor is in the same direction asthe resultant H of the original pair. This requires that the remaininggyro be reoriented to +90 or 90 (depending on which gyro has failed) inthe initial condition, and thereafter performs the same over-allfunction as the original pair but with constant angular momentum ratherthan variable. The initial angles of the two gyros of the remaining pairmust also be changed for the initial condition so as to maintain abalance between H, and H,,. Thus, the remaining gyros are reoriented to1'30". The net angular momentum of the system as a whole is controlledby the steering law, as described above, except that only the intactpair can be changed in magnitude in the x direction.

Vehicle attitude may be controlled by controlling the net angularmomentum of the CMG configuration, or by controlling its timederivative. In terms of the reference system described above, theprojections, H {H,,, H,,, H,}, of the net angular momentum vector, H, ofthe CMG system, onto the vehicle axes, are given by:

where h is the angular momentum magnitude of each gyro (all equal), andwhere S, sin a and C cos 01,, etc. The torque, T= {T T,,, T produced bythe CMG system on the vehicle is then given by T: H on where H =II I H[1,}, where and where w {(0 w,,, (1),} is the set of projections of thevehicle angular velocity vector 6, in inertial space, onto the vehicleaxes.

A desired torque, T, can then be produced by the CMG system if H' iscontrolled to follow a command, H given by H, T, 0H

where T is the control torque commanded by some control law. ().H can becomputed by equations (3) and (1) from gimbal angles and body-ratesignals, but in many important cases this term is so small that it canbe ignored. In other cases it is preferable to command H,. instead of7",. Taking the derivative of equation (I yields v l 4 u 2 le Me l l 201 2 2 I yi. lto w 'l'l. a 4 2 z m.

Inserting equation (6) into equation (5) yields, when dz di the actual Hobtained under this simple steering law:

= V 2/4, and K, K, b to produce the commanded angular rates (61,, d d61,) for each of the four CMGs. When a CMG fails, such as number i,switches *4 s, sits, s a t-sl-si si- When a=a the above matrix equalsthe identity matrix. As disturbance torque integrals on the vehicleaccumulate, a will wander away from (t and the CMG system will producecross-axis torques on the vehicle. When the. gimbal angles are sodifferent from a that the cross coupling becomes excessive, the CMGsystem is desaturated. In order to insure that the gimbal angles do notgo'to an unstable condition, mechanical and electrical stops areprovided.

With one of the gyros failed, only one solution to equation (5) exists.The initial gimbal angles for the failed mode where gyro number i hasfailed is a +30", 30, +30,-30}except that gryo number i :2 is chagned to(l), 90,and gryo number i is, of course, ignored. For example, if gyronumber 3 has failed a {90, 30, -30l. The solution to equation for a dwith a, 0 (where gyro number i has failed) is given by:

H 11,, at:

in either of a pair, and two CMGs can serve as standbys for at-least onefailure in any of the four operating CMGs.

The operation of the constant gain steering law presented above may bepresented pictorially through the diagram of FIG. 3. With no failures,all the switches are closed and the commanded angular monemtum rates 1HH H for each axis are modified by the respective constant gain networks(K K K where K,

Si and Si are opened and the values of the respective constant gainnetworks are altered to K,, 1/ 3 and K K l/ 2 In changing from theno-failure mode to a one-failure mode, the gimbal angles must also bechanged to the modified initial conditions, as previously described. Thefailed gyro should be de-spun to inhibit it from contributing oroffsetting the effect of the remaining CMGs. The steering lawmodification due to failure may be further simplified by not changingthe gains K K,,, K,. The resulting loss in the attitude control-loopgain will be reduced by 30 percent in the x-axis and 29 percent in the yand z-axis. In some applications such a loss of gain 'may be acceptable,and thereby simplify the computational operation of implementing theconstant gain steering law.

With the constant gain steering law,cross axis torques are producedunder simultaneous multiple axis commands or when the system hasabsorbed disturbance angular momentum. In some applications. the vehcileouter control loop is sufficient to remove the attitude errors producedby such cross axis torques. When this is not sufficient, the constantgain steering law can be upgraded by the addition of feedbackcomputations. The pseudo-torque feedback steering law effectivelyeliminates the cross coupling present with the constant gain law at theexpense of added circuit complexity, as shown in FIG. 4. A linearizedelectronic analog of the CMG transforamtion (equation 5) is created byapplying the commanded rates (61,, 6: d 6: to a gyro transfer matrix 10{B} which represents the gyro configuration. This matrix is a fucntionof the sine and cosine of the gyro gimbal angles. Therefore, the sineand cosine of each gimbal angle are computed through integrator 18 andsin/cos generator 19 to generate this transfer matrix 10. The matrixoutput is the electrically derived H} or pseudo-torque", representingthe H applied to the vehicle. It is fed back to be compared with thecommanded H at summers 12, 13, 14. If an error exists, integrators 15,l6, 17 correct the input to the constant gain steering law computer 11so that a set of gimbal rates 61, 51 64 61 are obtained which create thedesired torque combination.

This pseudo-torque feedback signal acts to correct the input to theconstant gain steering law computer 11 instead of requireing the outervehicle loop to make the necessary response. The torque feedback looprespone is adjusted to be much faster than the vehicle loop and gimballoop response. The torque feedback loop, therefore, serves as a highbandwidth computer which rapidly solves for a correct set of gimbalrates in response to H,. The CMG gimbal rate loops are thereforepresented with the correct commands to generate output torques withoutcross-coupling.

The electronic analog matrix {B} is linearized, except for trigonometricfunctions, and therefore, does not represent the gimbal loopnon-linearitites. These differences between the analog model and theactual hardware may result in small cross-coupling torques which areremoved by the outer vehicle loop. In applications where the gyro gimbalrate loop bandwidth is significantly higher than the vehcile loopbandwidth, the actual gimbal rates could be used to derive thepseudotorques and hence include any non-linearities inherent in the CMGhardware. When the disturbances require a gimbal loop bandwidthapproximately equal to the outer loop bandwidth, the pseuod-torque isderived as a function of commanded gimbal rates, as shown in FIG. 4, toattain a rapid response loop.

An alternate mechanization is to mount a resolver on each CMG gimbal andderive the [1,, sin a, and 02,, cos a, signals directly from the CMGgimbal angles. This technique eliminates entirely the need for computingnon-linear trigonometric functions and multiplications. The practicalrange of operation for the gimbal angles under the above steering law is:40 about 01 when all four gyros are operating. The CMG system can thendeliver approximately :t1.82h in the x-axis and approximately :1 .35h inthe y or z-axes. The momentum envelope has approximately the shape of anoctahedron with its six corners located on the coordinate axes. When CMGnumber 1 has failed, practical gimbal angle limits for CMG number 3 areat i85 about (1 90 and for the other two, at +25 and 55 about a 30. Themomentum envelope has a very irregular shape, intersecting the +1: axisat approximately 0.83h, and the x at approximately 0.99h. The envelopepeaks in the y and 1 directions are approximately located at H, 0.75hand H, H :1 .21h.

For certain applications it is possible to extend the envelope in thex-direction to almost i4n with four CMGs by some relatively simplemodifications in the constant gain steering law (which is also thefeedforward portion of the pseudo-torque feedback steering law). Insimple termns, such modifications amount to permitting a, and a to gonegative and a and a, to go positive so that all four CMG angularmomentum vecotrs can ultimately align in the same direction. Themomentum envelope for the simplest forms of such a steering lawmodifications (polarity reversals and limiters) will, however, possess abottle neck at about lH,,l 2h (or less). This bottle neck does notpresent a problem when the purpose for the vehicle attitude maneuvers isto attain various fixed attitudes; if the purpose is to track a movingattitude target, however, the momentum bottle neck may not be desirable.By further increasing the steering law complexity it is possible toeliminate the bottle neck effect.

The 4-FACS configuration is also suitable when a complex steering law,such as the pseudo inverse steering law with hangup avoidance, can beimplemented, especially when most of the required angular momentumcapacity is in one axis. Other configurations which require relativelycomplex steering law computations, cannot deliver all of their totalangular momentum in one direction, as is possible with a 4-FACSconfiguration.

The previously described steering laws may be implemented in a CMGattitude maneuvering control system as shown in FIG. 5. The maneuveringcommand computer 51 generates the vehicle acceleration commands for adesired maneuver. This command, m is fed to summer 52 and to integrator53. The integrated acceleration command, or rate command (b is fed tosummers 54 and 55. The vehicle rate to is sensed by the vehicle attitudesensors depicted in unit 66 and also fed to summer 54 and S5. The outputof summer 55 is fed to the Euler angle computer 56 which generatesattitude error Euler-angles, s. The error Euler angle is operated uponby a gain network 57 and summed with the other inputs to summer 54. Theoutput of summer 54 is operated upon by a gain network 58 and summedwith the acceleration command in summer 52. The output of summer 52 isthe commanded vehicle acceleration, (1),. which is multiplied by thevehicle inertia 59 and fed to summer 60. The output of summer 60represents the commanded net angular momentum rate, H to be acted uponby the steering law computer 61 such that the H of the CMG configurationapproximates H,. The output of computer 61, as previously discussed,represents the commanded angular rate, 61,, for orienting the respectivegimbals of the 4-FACS configuration. The actual gimbal angles of the CMGconfiguration 62 may be fed back to the steering law computer to correctfor cross coupling effects if so desired. The net gyroscopic torquecomputer 63, responsive to both the vehicle angular rate and the gimbalangles of the CMG configuration, may be employed to provide additionalinput to summing junction 60 to further refine the commanded angularmomentum rate but in many applications this signal is negligible. Theoutput of the CMG configuration 62 represents a torque T on the ve--hicle 64, subject to being summed at summing junction 65 with anydisturbance torques, T Ultimately, the output of summer 65 representsthe totality of the torques acting upon the vehicle to reorient thevehicle in response to a commanded maneuver.

While the invention has been described in its preferred embodiment, itis to be understood that the words which have been used are words ofdescription rather than limitation and that changes within the purviewof the appended claims may be made without departing from the true scopeand spirit of the invention in its broader aspects.

I claim:

1. An attitude control system for controlling the attitude of a vehiclecomprising a first pair of control moment gyroscopes,

a second pair of control moment gyroscopes, wherein the gimbal axes ofsaid first pair of control moment gyroscopes are essentially parallel,the gimbal axes of said second pair of control moment gyroscopes areessentially parallel, the net angular momentum vectorof said first pairhas a predetermined value at an initial condition that is equal andopposite to a corresponding predetermined value of the net angularmomentum of said second pair,

means for controlling the amplitude and direction of the net angularmomentum of each of said pair of control moment gyroscopes from saidinitial condition, whereby the net angular momentum vector of thecontrol system may be modified, and

means for controlling the angular rate of each of the gimbals in saidpairs of control moment gyroscope in accordance with a steering law ofthe form:

a 1 1 I It, a (1,, l/h l -1 1 K, 13,, a I -,1 l K, H a 1 l 1 wherein (iis the commanded gimbal rate of the identified gyro,

h is the angular momentum of each gyro, all equal,

H is the commanded angular rate of the vehicle about the identifiedaxis,

K K K are gain constants having values depending upon the angularorientations of the gyro gimbal axes relative to the identified vehicleaxes.

2. An attitude control system forcontrolling the attitude of a vehiclecomprising I a first pair of control moment gyroscopes,

a second pair of control moment gyroscopes, wherein the net angularmomentum vector of said first pair has a predetermined value at aninitial condition that is equal and opposite to a correspondingpredetermined value of the net angular momentum vector of said secondpair,

means for controlling the amplitude and direction of the net angularmomentum of each of said pair of control moment gyrocopes from saidinitial condition, whereby the net angular momentum vector of thecontrol system may be modified, and

means responsive to failure of any one of the gyroscopes for modifyingsaid initial condition of the remaining gyro of the failed pair and thatof the remaining pair of gyros. 3. The control system as claimed inclaim 2 including means'for controlling the angular rate of each of theoperative gyros in said pairs of control moment gyroscopes in accordancewith a steering law of the form ir I l a] x z rr a, 1 --1 K,,'H,,,. l/ha I l l K 'H a l 1 wherein d is the commanded'gimbal rate of theidentified y h is the angular momentum of eachgyro, all equal, H is thecommanded angular rate of the vehicle about the identified axis, and K,,K,,, K, are gain constants having values depending upon the angularorientations of the gyro gimbal axes relative to the identified vehicleaxes and modified fora failed gyro, and wherein the row of the 4 X 3matrix corresponding to the failed gyro is zero.

1. An attitude control system for controlling the attitude of a vehiclecomprising a first pair of control moment gyroscopes, a second pair ofcontrol moment gyroscopes, wherein the gimbal axes of said first pair ofcontrol moment gyroscopes are essentially parallel, the gimbal axes ofsaid second pair of control moment gyroscopes are essentially parallel,the net angular momentum vector of said first pair has a predeterminedvalue at an initial condition that is equal and opposite to acorresponding predetermined value of the net angular momentum of saidsecond pair, means for controlling the amplitude and direction of thenet angular momentum of each of said pair of control moment gyroscopesfrom said initial condition, whereby the net angular momentum vector ofthe control system may be modified, and means for controlling theangular rate of each of the gimbals in said pairs of control momentgyroscope in accordance with a steering law of the form: Alpha 1c 1 1 -1Kx Hxc Alpha 2c 1/h 1 -1 -1 Ky Hyc Alpha 3c 1 -1 1 Kz Hzc Alpha 4c 1 1 1wherein Alpha c is the commanded gimbal rate of the identified gyro, his the angular momentum of each gyro, all equal, H is the commandedangular rate of the vehicle about the identified axis, Kx, Ky, Kz aregain constants having values depending upon the angular orientations ofthe gyro gimbal axes relative to the identified vehicle axes.
 2. Anattitude control system for controlling the attitude of a vehiclecomprising a first pair of control moment gyroscopes, a second pair ofcontrol moment gyroscopes, wherein the net angular momentum vector ofsaid first pair has a predetermined value at an initial condition thatis equal and opposite to a corresponding predetermined value of the netangular momentum vector of said second pair, means for controlling theamplitude and direction of the net angular momentum of each of said pairof control moment gyrocopes from said initial condition, whereby the netangular momentum vector of the control system may be modified, and meansresponsive to failure of any one of the gyroscopes for modifying saidinitial condition of the remaining gyro of the failed pair and that ofthe remaining pair of gyros.
 3. The control system as claimed in claim 2including means for controlling the angular rate of each of theoperative gyros in said pairs of control moment gyroscopes in accordancewith a steering law of the form Alpha 1c 1 1 -1 Kx''Hxc Alpha 2c 1 -1 -1Ky''Hyc 1/h Alpha 3c 1 -1 1 Kz''Hxc Alpha 4c 1 1 1 wherein Alpha c isthe commanded gimbal rate of the identified gyro, h is the angularmomentum of each gyro, all equal, H is the commanded angular rate of thevehicle about the identified axis, and Kx'', Ky'', Kz'' are gainconstants having values depending upon the angular orientations of thegyro gimbal axes relative to the identified vehicle axes and modifiedfor a failed gyro, and wherein the row of the 4 X 3 matrix correspondingto the failed gyro is zero.